Plane elasticity problem of two-dimensional octagonal quasicrystals and crack problem
Plane elasticity problem of two-dimensional octagonal quasicrystals and crack problem
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DOI：
10.1088/1009-1963/10/8/315
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发表时间：
2001-08
期刊：
影响因子：
--
通讯作者：
Wang-min Zhou;Tian-you Fan
中科院分区：
文献类型：
--
作者：
Wang-min Zhou;Tian-you Fan
本文发展了二维八角准晶的平面弹性理论。通过引入位移函数，准晶体的平面弹性问题被简化为单个高阶偏微分方程。以材料中I型Griffith裂纹为例，利用傅里叶变换和对偶积分方程理论得到材料中I型Griffith裂纹的精确解析解，然后可以计算位移场和应力场、应力强度因子和应变能释放率。弄清楚了结果相对于相子的物理意义以及晶体和准晶体中裂纹问题的力学行为之间的差异。这些为研究新固相的变形和断裂提供了重要信息。
The plane elasticity theory of two-dimensional octagonal quasicrystals is developed in this paper. The plane elasticity problem of quasicrystals is reduced to a single higher-order partial differential equation by introducing a displacement function. As an example, the exact analytic solution of a Mode I Griffith crack in the material is obtained by using the Fourier transform and dual integral equations theory, then the displacement and stress fields, stress intensity factor and strain energy release rate can be calculated. The physical significance of the results relative to the phason and the difference between the mechanical behaviours of the crack problem in crystals and quasicrystals are figured out. These provide important information for studying the deformation and fracture of the new solid phase.